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NDA2010MathematicsDefinite IntegrationActual

What is the value of ₁^2 e^x ( 1 x - 1 x^2 ) d x

Options

  1. Ae ( e 2 -1 )
  2. Be(e-1)
  3. Ce- 1 e
  4. D0

Correct answer

A. e ( e 2 -1 )

Step-by-step solution

aligned & ₁^2 ( e^x x - e^x x^2 ) d x & = ₁^2 e^x x d x- ₁^2 e^x x^2 d x & = [ 1 x e^x ]₁^2- ₁^2- 1 x^2 e^x d x- ₁^2 e^x x^2 d x & = 1 2 e^2-e^1=e ( e 2 -1 ) aligned

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